# Could I get a longer wrench please?

**Classical Mechanics**Level 5

A fastener is a system of 2 objects - a bolt and a nut. You come across such a bolt/nut system tightened all the way, so that the nut and the top of the bolt are pressing against each other with a force of 5 N. If the nut is held fixed, how much torque **in mJ** does one need to put on the bolt to begin to unscrew it?

**Details and assumptions**

- The radius of the bolt is \(R = 2\) mm.
- The threads on the bolt are such that the bolt needs to rotate N = 20 cycles to move \(d = 1~cm\) vertically away from the nut.
- The friction coefficient between the bolt and nut is \(k = 0.5 \).